Over 400,000 people visited Farnam Street last month to learn howto make better decisions, create new ideas, and avoid stupid errors. With more than 100,000 subscribers to our popular weekly digest, we've become an online intellectual hub. To learn more about we what do, start here.

My first helpful notion is that it is usually best to simplify problems by deciding big “no-brainer” questions first.

***2. Numerical Fluency

The second helpful notion mimics Galileo’s conclusion that scientific reality is often revealed only by math, as if math was the language of God. Galileo’s attitude also works well in messy practical life. Without numerical fluency, in the part of life most of us inhabit, you are like a one-legged man in an ass-kicking contest.

***3. Invert

Inverting the problem won’t always solve it, but it will help you avoid trouble. Call it the avoiding stupidity filter.

The third helpful notion is that it is not enough to think problems through forward. You must also think in reverse, much like the rustic who wanted to know where he was going to die so that he’d never go there. Indeed, many problems can’t be solved forward. And that is why the great algebraist, Carl Jacobi, so often said: “invert, always invert.” And why Pythagoras thought in reverse to prove that the square root of two was an irrational number.

The fourth helpful notion is that the best and most practical wisdom is elementary academic wisdom. But there is one extremely important qualification: you must think in a multidisciplinary manner. You must routinely use all the easy-to-learn concepts from the freshman course in every basic subject. Where elementary ideas will serve, your problem solving must not be limited, as academia and many business bureaucracies are limited, by extreme balkanization into disciplines and subdisciplines, with strong taboos against any venture outside assigned territory. …

If, in your thinking, you rely on others, often through purchase of professional advice, whenever outside a small territory of your own, you will suffer much calamity.

This happens in part because professional advisors are often undone, not by their conscious malfeasance rather by troubles found in their subconscious bias.

His cognition will often be impaired, for your purposes, by financial incentives different from yours. And he will also suffer from the psychological defect caught by the proverb: to a man with a hammer, every problem looks like a nail.”

***5. Lollapalooza Effects

And you need to combine really big things.

The fifth helpful notion is that really big effects, lollapalooza effects, will often come only from large combinations of factors. For instance, tuberculosis was tamed, at least for a long time, only by routine combined use in each case of three different drugs. And other lollapalooza effects, like the flight of an airplane, follow a similar pattern.